Analysis of the linear viscoelasticity theory capabilities to simulate hydrostatic pressure influence on creep curves and lateral contraction ratio of rheonomous materials

A. V. Khokhlov

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 23 (2019) no. 2, pp. 304-340

Résumé

The Boltzmann–Volterra linear constitutive equation for isotropic non-aging visco-elastic materials is studied analytically in order to examine its capabilities to provide an adequate qualitative description of rheological phenomena related to creep under uni-axial loading combined with constant hydrostatic pressure and of evolution types of the Poisson's ratio (lateral contraction ratio) in creep. The constitutive equation does not involve the third invariants of stress and strain tensors and implies that their hydrostatic and deviatoric parts do not depend on each other. It is governed by two material functions of a positive real argument (that is shear and bulk creep compliances); they are implied to be positive, differentiable, increasing and convex up functions. General properties and characteristic features of the creep curves for volumetric, longitudinal and lateral strain produced by the linear theory (with an arbitrary shear and bulk creep functions) under constant tensile load and constant hydrostatic pressure are investigated. Conditions for creep curves monotonicity and for existence of extrema and sign changes of strains are studied. The Poisson's ratio evolution in time and its dependences on pressure and tensile stress levels and on qualitative characteristics of two creep functions are analyzed. Taking into account compressibility, volumetric creep and pressure influence (governed by the bulk creep function) affects strongly the qualitative behavior of longitudinal creep curves and the Poisson's ratio evolution and its range. In particular, it is proved that the linear theory can simulate non-monotone behavior and sign changes of lateral strain and Poisson’s ratio under constant tensile load (even if the pressure is zero) and the longitudinal strain may start to decrease provided the pressure level is high enough. The expressions for Poisson’s ratio via the strain triaxiality ratio (which is equal to volumetric strain divided by deviatoric strain) and in terms of pressure ratio to axial stress and the creep functions ratio are derived. Assuming creep functions are arbitrary (permissible), general accurate two-sided bounds for the Poisson's ratio range are obtained and the influence of pressure level on the range is studied. Additional restrictions on material functions and loading parameters are derived to provide negative values of Poisson’s ratio. Criteria for the Poisson’s ratio increase or decrease and for its non-dependence on time are found. The analysis revealed the set of immanent features and quantitative characteristics of the theoretic creep curves families and the Poisson's ratio dependence on time and pressure to axial stress ratio which are convenient to check in creep tests (with various levels of pressure and tensile stress) and can be employed as indicators of the linear viscoelasticity theory applicability (or non-applicability) for simulation of a material behavior. The specific properties and restrictions of the model with constant bulk creep compliance which simulates a material exhibiting purely elastic volumetric deformation are considered.

Détail

Keywords: viscoelasticity, volumetric creep, shear and bulk compliances, axial and lateral creep curves, lateral contraction ratio in creep, mean stress influence, indicators of linear range boundaries
Mots-clés : strain triaxiality ratio, negative Poisson’s ratio, identification.